SSC CGL Tier 2 (17 Feb) Past Year Paper (2018) | SSC CGL (Hindi) Tier - 1 Mock Test Series PDF Download

 Page 1


 
  
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
 (Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 17-2-2018] [Time : 10 AM to 12 PM 
1. What is the unit digit of the sum of first 111 
whole numbers? 
 ØeLece 111 hetCe& mebKÙeeDeeW kesâ Ùeesie keâe FkeâeF& Debkeâ keäÙee 
nw? 
 (a) 4 (b) 6 
 (c) 5 (d) 0 
2. How many 100 digit positive number are 
there? 
 100 DebkeâeW keâer efkeâleveer Oeveelcekeâ mebKÙeeSB nQ? 
 (a) 9 × 10
99
 (b) 9 × 10
100 
 (c) 10100 (d) 11 × 10
98 
3. What is the value of 
5.6 0.36 0.42 3.2
?
0.8 2.1
× + ×
×
 
 
5.6 0.36 0.42 3.2
0.8 2.1
× + ×
×
 keâe ceeve keäÙee nw? 
 (a) 2 (b) 1 
 (c) 3 (d) 3/2 
4. What is the value of 
 
–
– – –
3 3 3
2 2 2
(1.2) (0.8) (0.7) 2.016
?
(1.35) (1.2) (0.8) (0.7) 0.96 0.84 0.56
+ +
? ? + +
? ?
 
 
–
– – –
3 3 3
2 2 2
(1.2) (0.8) (0.7) 2.016
?
(1.35) (1.2) (0.8) (0.7) 0.96 0.84 0.56
+ +
? ? + +
? ?
 
 keâe ceeve keäÙee nw? 
 (a) 1/4 (b) 1/2 
 (c) 1 (d) 2 
5. What is the unit digit of  
 (217)
413
×(819)
547
×(414)
624
×(342)
812
? 
 (217)
413
×(819)
547
×(414)
624
×(342)
812
 keâe FkeâeF& Debkeâ 
keäÙee nw? 
 (a) 2 (b) 4 
 (c) 6 (d) 8 
6. What is the value of 
1 1
S
1 3 5 1 4
= + +
× × ×
 
 
1 1 1 1
...
3 5 7 4 7 5 7 9 7 10
+ + + +
× × × × × ×
upto 20 
terms, then what is the value of S? 
 
1 1 1 1
S
1 3 5 1 4 3 5 7 4 7
= + + + +
× × × × × ×
 
 
1 1
...
5 7 9 7 10
+ +
× × ×
20 heoeW lekeâ nQ, lees S keâe ceeve 
keäÙee nw? 
 (a) 6179/15275 (b) 6070/14973 
 (c) 7191/15174 (d) 5183/16423 
7. Which of the following is TRUE? 
 efvecveefueefKele ceW mes keâewve-mee melÙe nw? 
 I. 
3 4
1 1 1
12 29 5
> > 
 II. 
3 4
1 1 1
29 12 5
> > 
 III. 
3 4
1 1 1
5 12 29
> > 
 IV. 
3 4
1 1 1
5 29 12
> > 
 (a) Only I / kesâJeue  I  
 (b) Only II / kesâJeue  II  
 (c) Only III / kesâJeue  III  
 (d) Only IV / kesâJeue  IV  
8. N is the largest two digit number, which when 
divided by 3, 4 and 6 leaves the remainder 1, 2 
and 4 respectively. What is the remainder 
when N is divided by 5? 
 oes DebkeâeW keâer Skeâ meyemes yeÌ[er mebKÙee N nw, efpemes peye 3, 
4 leLee 6 mes efJeYeeefpele efkeâÙee peelee nw lees Mes<eHeâue 
›eâceMe: 1, 2 leLee 4 Deelee nw~ N keâes 5 mes efJeYeeefpele 
keâjves hej Mes<eHeâue keäÙee nw? 
 (a) 4 (b) 2 
 (c) 0 (d) 1 
9. Which of the following is TRUE? 
 efvecveefueefKele ceW mes keâewve-mee melÙe nw? 
 I. 
3 4
11 7 45 > > 
 II. 
3 4
7 11 45 > > 
 III. 
3 4
7 45 11 > > 
 IV. 
3 4
45 7 11 > > 
Page 2


 
  
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
 (Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 17-2-2018] [Time : 10 AM to 12 PM 
1. What is the unit digit of the sum of first 111 
whole numbers? 
 ØeLece 111 hetCe& mebKÙeeDeeW kesâ Ùeesie keâe FkeâeF& Debkeâ keäÙee 
nw? 
 (a) 4 (b) 6 
 (c) 5 (d) 0 
2. How many 100 digit positive number are 
there? 
 100 DebkeâeW keâer efkeâleveer Oeveelcekeâ mebKÙeeSB nQ? 
 (a) 9 × 10
99
 (b) 9 × 10
100 
 (c) 10100 (d) 11 × 10
98 
3. What is the value of 
5.6 0.36 0.42 3.2
?
0.8 2.1
× + ×
×
 
 
5.6 0.36 0.42 3.2
0.8 2.1
× + ×
×
 keâe ceeve keäÙee nw? 
 (a) 2 (b) 1 
 (c) 3 (d) 3/2 
4. What is the value of 
 
–
– – –
3 3 3
2 2 2
(1.2) (0.8) (0.7) 2.016
?
(1.35) (1.2) (0.8) (0.7) 0.96 0.84 0.56
+ +
? ? + +
? ?
 
 
–
– – –
3 3 3
2 2 2
(1.2) (0.8) (0.7) 2.016
?
(1.35) (1.2) (0.8) (0.7) 0.96 0.84 0.56
+ +
? ? + +
? ?
 
 keâe ceeve keäÙee nw? 
 (a) 1/4 (b) 1/2 
 (c) 1 (d) 2 
5. What is the unit digit of  
 (217)
413
×(819)
547
×(414)
624
×(342)
812
? 
 (217)
413
×(819)
547
×(414)
624
×(342)
812
 keâe FkeâeF& Debkeâ 
keäÙee nw? 
 (a) 2 (b) 4 
 (c) 6 (d) 8 
6. What is the value of 
1 1
S
1 3 5 1 4
= + +
× × ×
 
 
1 1 1 1
...
3 5 7 4 7 5 7 9 7 10
+ + + +
× × × × × ×
upto 20 
terms, then what is the value of S? 
 
1 1 1 1
S
1 3 5 1 4 3 5 7 4 7
= + + + +
× × × × × ×
 
 
1 1
...
5 7 9 7 10
+ +
× × ×
20 heoeW lekeâ nQ, lees S keâe ceeve 
keäÙee nw? 
 (a) 6179/15275 (b) 6070/14973 
 (c) 7191/15174 (d) 5183/16423 
7. Which of the following is TRUE? 
 efvecveefueefKele ceW mes keâewve-mee melÙe nw? 
 I. 
3 4
1 1 1
12 29 5
> > 
 II. 
3 4
1 1 1
29 12 5
> > 
 III. 
3 4
1 1 1
5 12 29
> > 
 IV. 
3 4
1 1 1
5 29 12
> > 
 (a) Only I / kesâJeue  I  
 (b) Only II / kesâJeue  II  
 (c) Only III / kesâJeue  III  
 (d) Only IV / kesâJeue  IV  
8. N is the largest two digit number, which when 
divided by 3, 4 and 6 leaves the remainder 1, 2 
and 4 respectively. What is the remainder 
when N is divided by 5? 
 oes DebkeâeW keâer Skeâ meyemes yeÌ[er mebKÙee N nw, efpemes peye 3, 
4 leLee 6 mes efJeYeeefpele efkeâÙee peelee nw lees Mes<eHeâue 
›eâceMe: 1, 2 leLee 4 Deelee nw~ N keâes 5 mes efJeYeeefpele 
keâjves hej Mes<eHeâue keäÙee nw? 
 (a) 4 (b) 2 
 (c) 0 (d) 1 
9. Which of the following is TRUE? 
 efvecveefueefKele ceW mes keâewve-mee melÙe nw? 
 I. 
3 4
11 7 45 > > 
 II. 
3 4
7 11 45 > > 
 III. 
3 4
7 45 11 > > 
 IV. 
3 4
45 7 11 > > 
 
   
 (a) Only I / kesâJeue I  
 (b) Only II / kesâJeue II  
 (c) Only III / kesâJeue III  
 (d) Only IV / kesâJeue IV  
10. A and B are positive integers. If A + B + AB = 
65, then what is the difference between A and B 
(A, B = 15)? 
 A leLee B Oeveelcekeâ hetCeeËkeâ nw~ Ùeefo A+B+AB = 65 nw, 
lees A leLee B kesâ ceOÙe Deblej keäÙee nw (A, B = 15)? 
 (a) 3 (b) 4 
 (c) 5 (d) 6 
11. What is the value of 14
3
 + 16
3
 + 18
3
 + .... + 30
3
? 
 14
3
 + 16
3
 + 18
3
 + ....... + 30
3
 keâe ceeve keäÙee nw? 
 (a) 134576 (b) 120212 
 (c) 115624 (d) 111672 
12. What is the value of 
 4600 540 1280 250 36 ? + + + + 
 4600 540 1280 250 36 ? + + + + keâe ceeve 
keäÙee nw? 
 (a) 69 (b) 68 
 (c) 70 (d) 72 
13. If x + y + z = 0, then what is the value of 
(3y
2
+x
2
+z
2
)/(2y
2
–xz)? 
 Ùeefo x + y + z = 0 nes, lees (3y
2
 + x
2
 + z
2
)/(2y
2
–xz) 
keâe ceeve keäÙee nw? 
 (a) 2 (b) 1 
 (c) 3/2 (d) 5/3 
14. If P = 7+4v3 and PQ = 1, then what is the value 
of 1/p
2
 + 1/Q
2
? 
 Ùeefo P = 7+4v3 leLee PQ = 1 nw, lees 1/p
2
 + 1/Q
2 
keâe 
ceeve keäÙee nw? 
 (a) 196 (b) 194 
 (c) 206 (d) 182 
15. If a
3
+3a
2
+9a = 1, then what is the value of a
3
 + 
(3/a)? 
 Ùeefo a
3
+3a
2
+9a = 1 nes, lees a
3
 + (3/a) keâe ceeve keäÙee 
nw? 
 (a) 31 (b) 26 
 (c) 28 (d) 24 
16. x, y and z are real numbers. If x
3
+y
3
+z
3
 = 13, x 
+ y + z = 1 and xyz = 1, then what is the value 
of xy + yz + zx? 
 x, y leLee z JeemleefJekeâ mebKÙeeSB nQ~ Ùeefo  x
3
+y
3
+z
3
 = 
13, x + y + z = 1 leLee xyz = 1 nw, lees xy + yz + zx 
keâe ceeve keäÙee nw? 
 (a) – 1 (b) 1 
 (c) 3 (d) – 3 
17. If (a + b)/c = 6/5 and (b + c)/a = 9/2, then what 
is the value of (a + c)/b? 
 Ùeefo (a + b)/c = 6/5 Deewj (b + c)/a = 9/2 nw, lees (a + 
c)/b keâe ceeve keäÙee nw? 
 (a) 9/5 (b) 11/7 
 (c) 7/11 (d) 7/4 
18. If x
3
 + y
3
 + z
3
 = 3(1+xyz), P = y + z – x, Q = z + 
x –y and R = x + y – z, then what is the value of 
p
3
+Q
3
+R
3
–3PQR? 
 Ùeefo x
3
 + y
3
 + z
3
 = 3(1+xyz), P = y + z – x, Q = z 
+ x –y Deewj R = x + y – z, nw, lees p
3
+Q
3
+R
3
–3PQR 
keâe ceeve keäÙee nw? 
 (a) 9 (b) 8 
 (c) 12 (d) 6 
19. If x
1
x
2
x
3
 = 4(4+x
1
+x
2
+x
3
), then what is the value 
of [1/(2+x
1
)] + [1/(2+x
2
)] + [1/(2+x
3
)]? 
 Ùeefo x
1
x
2
x
3
 = 4(4+x
1
+x
2
+x
3
), nes, lees [1/(2+x
1
)] + 
[1/(2+x
2
)] + [1/(2+x
3
)] keâe ceeve keäÙee nw? 
 (a) 1 (b) 1/2 
 (c) 2 (d) 1/3 
20. If a and ß are the roots of equation x
2
–x+1= 0, 
then which equation will have roots a
3
 and ß
3
? 
 Ùeefo a leLee ß meceerkeâjCe x
2
–x+1=0 kesâ cetue nQ, lees 
efkeâme meceerkeâjCe kesâ cetue a
3
 leLee ß
3
 neWies? 
 (a) x
2 
+ 2x + 1 = 0 
 (b) x
2 
– 2x – 1 = 0 
 (c) x
2 
+ 3x – 1 = 0 
 (d) x
2 
– 3x + 1 = 0 
21. If 3x + 5y + 7z = 49 and 9x + 8y + 21z = 126, 
then what is the value of y? 
 Ùeefo 3x + 5y + 7z = 49 leLee 9x + 8y + 21z = 126, 
nw, lees y keâe ceeve keäÙee nw? 
 (a) 4 (b) 2 
 (c) 3 (d) 5 
22. Cost of 4 pens, 6 note books and 9 files is Rs. 
305. Cost of 3 pens, 4 notebooks and 2 files is 
Rs. 145. What is the cost (in Rs) of 5 pens, 8 
notebooks and 16 files? 
 4 keâuece, 6 veesšyegkeâ leLee 9 HeâeFue keâe cetuÙe 305 ®0 
nw~ 3 keâuece, 4 veesšyegkeâ leLee 2 HeâeFue keâe cetuÙe 145 
®0 nw~ 5 keâuece, 8 veesšyegkeâ leLee 16 HeâeFue keâe cetuÙe 
(®0 ceW) keäÙee nw? 
 (a) 415 
 (b) 465 
 (c) 440 
 (d) Cannot be determined / %eele veneR efkeâÙee pee mekeâlee 
Page 3


 
  
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
 (Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 17-2-2018] [Time : 10 AM to 12 PM 
1. What is the unit digit of the sum of first 111 
whole numbers? 
 ØeLece 111 hetCe& mebKÙeeDeeW kesâ Ùeesie keâe FkeâeF& Debkeâ keäÙee 
nw? 
 (a) 4 (b) 6 
 (c) 5 (d) 0 
2. How many 100 digit positive number are 
there? 
 100 DebkeâeW keâer efkeâleveer Oeveelcekeâ mebKÙeeSB nQ? 
 (a) 9 × 10
99
 (b) 9 × 10
100 
 (c) 10100 (d) 11 × 10
98 
3. What is the value of 
5.6 0.36 0.42 3.2
?
0.8 2.1
× + ×
×
 
 
5.6 0.36 0.42 3.2
0.8 2.1
× + ×
×
 keâe ceeve keäÙee nw? 
 (a) 2 (b) 1 
 (c) 3 (d) 3/2 
4. What is the value of 
 
–
– – –
3 3 3
2 2 2
(1.2) (0.8) (0.7) 2.016
?
(1.35) (1.2) (0.8) (0.7) 0.96 0.84 0.56
+ +
? ? + +
? ?
 
 
–
– – –
3 3 3
2 2 2
(1.2) (0.8) (0.7) 2.016
?
(1.35) (1.2) (0.8) (0.7) 0.96 0.84 0.56
+ +
? ? + +
? ?
 
 keâe ceeve keäÙee nw? 
 (a) 1/4 (b) 1/2 
 (c) 1 (d) 2 
5. What is the unit digit of  
 (217)
413
×(819)
547
×(414)
624
×(342)
812
? 
 (217)
413
×(819)
547
×(414)
624
×(342)
812
 keâe FkeâeF& Debkeâ 
keäÙee nw? 
 (a) 2 (b) 4 
 (c) 6 (d) 8 
6. What is the value of 
1 1
S
1 3 5 1 4
= + +
× × ×
 
 
1 1 1 1
...
3 5 7 4 7 5 7 9 7 10
+ + + +
× × × × × ×
upto 20 
terms, then what is the value of S? 
 
1 1 1 1
S
1 3 5 1 4 3 5 7 4 7
= + + + +
× × × × × ×
 
 
1 1
...
5 7 9 7 10
+ +
× × ×
20 heoeW lekeâ nQ, lees S keâe ceeve 
keäÙee nw? 
 (a) 6179/15275 (b) 6070/14973 
 (c) 7191/15174 (d) 5183/16423 
7. Which of the following is TRUE? 
 efvecveefueefKele ceW mes keâewve-mee melÙe nw? 
 I. 
3 4
1 1 1
12 29 5
> > 
 II. 
3 4
1 1 1
29 12 5
> > 
 III. 
3 4
1 1 1
5 12 29
> > 
 IV. 
3 4
1 1 1
5 29 12
> > 
 (a) Only I / kesâJeue  I  
 (b) Only II / kesâJeue  II  
 (c) Only III / kesâJeue  III  
 (d) Only IV / kesâJeue  IV  
8. N is the largest two digit number, which when 
divided by 3, 4 and 6 leaves the remainder 1, 2 
and 4 respectively. What is the remainder 
when N is divided by 5? 
 oes DebkeâeW keâer Skeâ meyemes yeÌ[er mebKÙee N nw, efpemes peye 3, 
4 leLee 6 mes efJeYeeefpele efkeâÙee peelee nw lees Mes<eHeâue 
›eâceMe: 1, 2 leLee 4 Deelee nw~ N keâes 5 mes efJeYeeefpele 
keâjves hej Mes<eHeâue keäÙee nw? 
 (a) 4 (b) 2 
 (c) 0 (d) 1 
9. Which of the following is TRUE? 
 efvecveefueefKele ceW mes keâewve-mee melÙe nw? 
 I. 
3 4
11 7 45 > > 
 II. 
3 4
7 11 45 > > 
 III. 
3 4
7 45 11 > > 
 IV. 
3 4
45 7 11 > > 
 
   
 (a) Only I / kesâJeue I  
 (b) Only II / kesâJeue II  
 (c) Only III / kesâJeue III  
 (d) Only IV / kesâJeue IV  
10. A and B are positive integers. If A + B + AB = 
65, then what is the difference between A and B 
(A, B = 15)? 
 A leLee B Oeveelcekeâ hetCeeËkeâ nw~ Ùeefo A+B+AB = 65 nw, 
lees A leLee B kesâ ceOÙe Deblej keäÙee nw (A, B = 15)? 
 (a) 3 (b) 4 
 (c) 5 (d) 6 
11. What is the value of 14
3
 + 16
3
 + 18
3
 + .... + 30
3
? 
 14
3
 + 16
3
 + 18
3
 + ....... + 30
3
 keâe ceeve keäÙee nw? 
 (a) 134576 (b) 120212 
 (c) 115624 (d) 111672 
12. What is the value of 
 4600 540 1280 250 36 ? + + + + 
 4600 540 1280 250 36 ? + + + + keâe ceeve 
keäÙee nw? 
 (a) 69 (b) 68 
 (c) 70 (d) 72 
13. If x + y + z = 0, then what is the value of 
(3y
2
+x
2
+z
2
)/(2y
2
–xz)? 
 Ùeefo x + y + z = 0 nes, lees (3y
2
 + x
2
 + z
2
)/(2y
2
–xz) 
keâe ceeve keäÙee nw? 
 (a) 2 (b) 1 
 (c) 3/2 (d) 5/3 
14. If P = 7+4v3 and PQ = 1, then what is the value 
of 1/p
2
 + 1/Q
2
? 
 Ùeefo P = 7+4v3 leLee PQ = 1 nw, lees 1/p
2
 + 1/Q
2 
keâe 
ceeve keäÙee nw? 
 (a) 196 (b) 194 
 (c) 206 (d) 182 
15. If a
3
+3a
2
+9a = 1, then what is the value of a
3
 + 
(3/a)? 
 Ùeefo a
3
+3a
2
+9a = 1 nes, lees a
3
 + (3/a) keâe ceeve keäÙee 
nw? 
 (a) 31 (b) 26 
 (c) 28 (d) 24 
16. x, y and z are real numbers. If x
3
+y
3
+z
3
 = 13, x 
+ y + z = 1 and xyz = 1, then what is the value 
of xy + yz + zx? 
 x, y leLee z JeemleefJekeâ mebKÙeeSB nQ~ Ùeefo  x
3
+y
3
+z
3
 = 
13, x + y + z = 1 leLee xyz = 1 nw, lees xy + yz + zx 
keâe ceeve keäÙee nw? 
 (a) – 1 (b) 1 
 (c) 3 (d) – 3 
17. If (a + b)/c = 6/5 and (b + c)/a = 9/2, then what 
is the value of (a + c)/b? 
 Ùeefo (a + b)/c = 6/5 Deewj (b + c)/a = 9/2 nw, lees (a + 
c)/b keâe ceeve keäÙee nw? 
 (a) 9/5 (b) 11/7 
 (c) 7/11 (d) 7/4 
18. If x
3
 + y
3
 + z
3
 = 3(1+xyz), P = y + z – x, Q = z + 
x –y and R = x + y – z, then what is the value of 
p
3
+Q
3
+R
3
–3PQR? 
 Ùeefo x
3
 + y
3
 + z
3
 = 3(1+xyz), P = y + z – x, Q = z 
+ x –y Deewj R = x + y – z, nw, lees p
3
+Q
3
+R
3
–3PQR 
keâe ceeve keäÙee nw? 
 (a) 9 (b) 8 
 (c) 12 (d) 6 
19. If x
1
x
2
x
3
 = 4(4+x
1
+x
2
+x
3
), then what is the value 
of [1/(2+x
1
)] + [1/(2+x
2
)] + [1/(2+x
3
)]? 
 Ùeefo x
1
x
2
x
3
 = 4(4+x
1
+x
2
+x
3
), nes, lees [1/(2+x
1
)] + 
[1/(2+x
2
)] + [1/(2+x
3
)] keâe ceeve keäÙee nw? 
 (a) 1 (b) 1/2 
 (c) 2 (d) 1/3 
20. If a and ß are the roots of equation x
2
–x+1= 0, 
then which equation will have roots a
3
 and ß
3
? 
 Ùeefo a leLee ß meceerkeâjCe x
2
–x+1=0 kesâ cetue nQ, lees 
efkeâme meceerkeâjCe kesâ cetue a
3
 leLee ß
3
 neWies? 
 (a) x
2 
+ 2x + 1 = 0 
 (b) x
2 
– 2x – 1 = 0 
 (c) x
2 
+ 3x – 1 = 0 
 (d) x
2 
– 3x + 1 = 0 
21. If 3x + 5y + 7z = 49 and 9x + 8y + 21z = 126, 
then what is the value of y? 
 Ùeefo 3x + 5y + 7z = 49 leLee 9x + 8y + 21z = 126, 
nw, lees y keâe ceeve keäÙee nw? 
 (a) 4 (b) 2 
 (c) 3 (d) 5 
22. Cost of 4 pens, 6 note books and 9 files is Rs. 
305. Cost of 3 pens, 4 notebooks and 2 files is 
Rs. 145. What is the cost (in Rs) of 5 pens, 8 
notebooks and 16 files? 
 4 keâuece, 6 veesšyegkeâ leLee 9 HeâeFue keâe cetuÙe 305 ®0 
nw~ 3 keâuece, 4 veesšyegkeâ leLee 2 HeâeFue keâe cetuÙe 145 
®0 nw~ 5 keâuece, 8 veesšyegkeâ leLee 16 HeâeFue keâe cetuÙe 
(®0 ceW) keäÙee nw? 
 (a) 415 
 (b) 465 
 (c) 440 
 (d) Cannot be determined / %eele veneR efkeâÙee pee mekeâlee 
 
   
23. ABC is a right angled triangle. ?BAC = 90
0
 
and ?ACB = 60
0
. What is the ratio of the 
circum radius of the triangle to the side AB? 
 ABC Skeâ mecekeâesCe ef$eYegpe nw~ ?BAC = 90
0
 leLee 
?ACB = 60
0
 nw~ ef$eYegpe keâer heefjef$epÙee keâe Yegpee AB 
mes keäÙee Devegheele nw? 
 (a) 1 : 2 (b) 1 : v3 
 (c) 2 : v3 (d) 2 : 3 
24. In the given figure, ABCD is a square whose 
side is 4 cm. P is a point on the side AD. What 
is the minimum value (in cm) of BP + CP? 
 oer ieF& Deeke=âefle ceW, ABCD Skeâ Jeie& nw efpemekeâer Yegpee 4 
mes.ceer. nw~ Yegpee AD hej P Skeâ efyevog nw~ BP + CP keâe 
vÙetvelece ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 4v5 (b) 4v4 
 (c) 6v3 (d) 4v6 
25. Triangle ABC is similar to triangle PQR and 
AB : PQ = 2 : 3. AD is the median to the side 
BC in triangle ABC and PS is the median to the 
side QR in triangle PQR. What is the value of 
(BD/QS)
2
? 
 ef$eYegpe ABC, ef$eYegpe PQR kesâ mece¤he nw leLee AB : 
PQ = 2 : 3 nw~ AD, ef$eYegpe ABC ceW Yegpee BC hej Skeâ 
ceeefOÙekeâe nw leLee PS, ef$eYegpe PQR ceW Yegpee QR hej 
Skeâ ceeefOÙekeâe nw~ (BD/QS)
2  
keâe ceeve keäÙee nw? 
 (a) 3/5 (b) 4/9 
 (c) 2/3 (d) 4/7 
26. In the given figure, B and C are the centres of 
the two circles. ADE is the common tangent to 
the two circles. If the ratio of the radius of both 
the circles is 3 : 5 and AC = 40, then what is the 
value of DE? 
 oer ieF& Deeke=âefle ceW, B leLee C oes Je=òeeW kesâ kesâvõ nQ~ 
ADE oesveeW Je=òeeW keâer Skeâ GYeÙeefve<" mheMe& jsKee nw~ Ùeefo 
oesveeW Je=òeeW keâer ef$epÙeeDeeW keâe Devegheele 3 : 5 nw leLee 
AC = 40 nw, lees DE keâe ceeve keäÙee nw? 
 
 (a) 3v15 (b) 5v15 
 (c) 6v15 (d) 4v15 
27. In the given figure, AB = 30 cm and CD = 24 
cm. What is the value (in cm) of MN? 
 oer ieF& Deeke=âefle ceW, AB = 30 mes.ceer. leLee CD = 24 
mes.ceer. nw~ MN keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 18 (b) 9 
 (c) 12 (d) 15 
28. AB and AC are the two tangents to a circle 
whose radius is 6 cm. If ?BAC = 60
0
, then what 
is the value (in cm) of v(AB
2
 + AC
2
)? 
 AB Deewj AC Skeâ Je=òe hej oes mheMe& jsKeeSB nQ efpemekeâer 
ef$epÙee 6 mes.ceer. nw~ Ùeefo ?BAC = 60
0 
nw, lees v(AB
2
 + 
AC
2
) keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 (a) 6v6 (b) 4v6 
 (c) 9v3 (d) 8v3 
29. In the given figure, ABC is a right angled 
triangle. ?ABC = 90
0 
and ?ACB = 60
0
. If the 
radius of the smaller circle is 2 cm, then what is 
the radius (in cm) of the larger circle? 
 oer ieF& Deeke=âefle ceW, ABC Skeâ mecekeâesCe ef$eYegpe nw~ 
?ABC = 90
0 
leLee ?ACB = 60
0
 nw~ Ùeefo Úesšs Je=òe 
keâer ef$epÙee 2 mes.ceer. nw, lees yeÌ[s Je=òe keâer ef$epÙee (mes.ceer. 
ceW) keäÙee nw? 
 
 (a) 4 (b) 6 
 (c) 4.5 (d) 7.5 
30. In the given figure, O is centre of the circle. 
Circle has 3 tangents. If ?QPR = 45
0
, then 
what is the value (in degrees) of ?QOR? 
 oer ieF& Deeke=âefle ceW, O Je=òe keâe kesâvõ nw~ Je=òe hej 3 mheMe& 
jsKeeSB nQ~ Ùeefo ?QPR = 45
0 
nw, lees ?QOR keâe ceeve 
(ef[«eer ceW) keäÙee nw? 
 
 (a) 67.5 (b) 72 
 (c) 78.5 (d) 65 
Page 4


 
  
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
 (Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 17-2-2018] [Time : 10 AM to 12 PM 
1. What is the unit digit of the sum of first 111 
whole numbers? 
 ØeLece 111 hetCe& mebKÙeeDeeW kesâ Ùeesie keâe FkeâeF& Debkeâ keäÙee 
nw? 
 (a) 4 (b) 6 
 (c) 5 (d) 0 
2. How many 100 digit positive number are 
there? 
 100 DebkeâeW keâer efkeâleveer Oeveelcekeâ mebKÙeeSB nQ? 
 (a) 9 × 10
99
 (b) 9 × 10
100 
 (c) 10100 (d) 11 × 10
98 
3. What is the value of 
5.6 0.36 0.42 3.2
?
0.8 2.1
× + ×
×
 
 
5.6 0.36 0.42 3.2
0.8 2.1
× + ×
×
 keâe ceeve keäÙee nw? 
 (a) 2 (b) 1 
 (c) 3 (d) 3/2 
4. What is the value of 
 
–
– – –
3 3 3
2 2 2
(1.2) (0.8) (0.7) 2.016
?
(1.35) (1.2) (0.8) (0.7) 0.96 0.84 0.56
+ +
? ? + +
? ?
 
 
–
– – –
3 3 3
2 2 2
(1.2) (0.8) (0.7) 2.016
?
(1.35) (1.2) (0.8) (0.7) 0.96 0.84 0.56
+ +
? ? + +
? ?
 
 keâe ceeve keäÙee nw? 
 (a) 1/4 (b) 1/2 
 (c) 1 (d) 2 
5. What is the unit digit of  
 (217)
413
×(819)
547
×(414)
624
×(342)
812
? 
 (217)
413
×(819)
547
×(414)
624
×(342)
812
 keâe FkeâeF& Debkeâ 
keäÙee nw? 
 (a) 2 (b) 4 
 (c) 6 (d) 8 
6. What is the value of 
1 1
S
1 3 5 1 4
= + +
× × ×
 
 
1 1 1 1
...
3 5 7 4 7 5 7 9 7 10
+ + + +
× × × × × ×
upto 20 
terms, then what is the value of S? 
 
1 1 1 1
S
1 3 5 1 4 3 5 7 4 7
= + + + +
× × × × × ×
 
 
1 1
...
5 7 9 7 10
+ +
× × ×
20 heoeW lekeâ nQ, lees S keâe ceeve 
keäÙee nw? 
 (a) 6179/15275 (b) 6070/14973 
 (c) 7191/15174 (d) 5183/16423 
7. Which of the following is TRUE? 
 efvecveefueefKele ceW mes keâewve-mee melÙe nw? 
 I. 
3 4
1 1 1
12 29 5
> > 
 II. 
3 4
1 1 1
29 12 5
> > 
 III. 
3 4
1 1 1
5 12 29
> > 
 IV. 
3 4
1 1 1
5 29 12
> > 
 (a) Only I / kesâJeue  I  
 (b) Only II / kesâJeue  II  
 (c) Only III / kesâJeue  III  
 (d) Only IV / kesâJeue  IV  
8. N is the largest two digit number, which when 
divided by 3, 4 and 6 leaves the remainder 1, 2 
and 4 respectively. What is the remainder 
when N is divided by 5? 
 oes DebkeâeW keâer Skeâ meyemes yeÌ[er mebKÙee N nw, efpemes peye 3, 
4 leLee 6 mes efJeYeeefpele efkeâÙee peelee nw lees Mes<eHeâue 
›eâceMe: 1, 2 leLee 4 Deelee nw~ N keâes 5 mes efJeYeeefpele 
keâjves hej Mes<eHeâue keäÙee nw? 
 (a) 4 (b) 2 
 (c) 0 (d) 1 
9. Which of the following is TRUE? 
 efvecveefueefKele ceW mes keâewve-mee melÙe nw? 
 I. 
3 4
11 7 45 > > 
 II. 
3 4
7 11 45 > > 
 III. 
3 4
7 45 11 > > 
 IV. 
3 4
45 7 11 > > 
 
   
 (a) Only I / kesâJeue I  
 (b) Only II / kesâJeue II  
 (c) Only III / kesâJeue III  
 (d) Only IV / kesâJeue IV  
10. A and B are positive integers. If A + B + AB = 
65, then what is the difference between A and B 
(A, B = 15)? 
 A leLee B Oeveelcekeâ hetCeeËkeâ nw~ Ùeefo A+B+AB = 65 nw, 
lees A leLee B kesâ ceOÙe Deblej keäÙee nw (A, B = 15)? 
 (a) 3 (b) 4 
 (c) 5 (d) 6 
11. What is the value of 14
3
 + 16
3
 + 18
3
 + .... + 30
3
? 
 14
3
 + 16
3
 + 18
3
 + ....... + 30
3
 keâe ceeve keäÙee nw? 
 (a) 134576 (b) 120212 
 (c) 115624 (d) 111672 
12. What is the value of 
 4600 540 1280 250 36 ? + + + + 
 4600 540 1280 250 36 ? + + + + keâe ceeve 
keäÙee nw? 
 (a) 69 (b) 68 
 (c) 70 (d) 72 
13. If x + y + z = 0, then what is the value of 
(3y
2
+x
2
+z
2
)/(2y
2
–xz)? 
 Ùeefo x + y + z = 0 nes, lees (3y
2
 + x
2
 + z
2
)/(2y
2
–xz) 
keâe ceeve keäÙee nw? 
 (a) 2 (b) 1 
 (c) 3/2 (d) 5/3 
14. If P = 7+4v3 and PQ = 1, then what is the value 
of 1/p
2
 + 1/Q
2
? 
 Ùeefo P = 7+4v3 leLee PQ = 1 nw, lees 1/p
2
 + 1/Q
2 
keâe 
ceeve keäÙee nw? 
 (a) 196 (b) 194 
 (c) 206 (d) 182 
15. If a
3
+3a
2
+9a = 1, then what is the value of a
3
 + 
(3/a)? 
 Ùeefo a
3
+3a
2
+9a = 1 nes, lees a
3
 + (3/a) keâe ceeve keäÙee 
nw? 
 (a) 31 (b) 26 
 (c) 28 (d) 24 
16. x, y and z are real numbers. If x
3
+y
3
+z
3
 = 13, x 
+ y + z = 1 and xyz = 1, then what is the value 
of xy + yz + zx? 
 x, y leLee z JeemleefJekeâ mebKÙeeSB nQ~ Ùeefo  x
3
+y
3
+z
3
 = 
13, x + y + z = 1 leLee xyz = 1 nw, lees xy + yz + zx 
keâe ceeve keäÙee nw? 
 (a) – 1 (b) 1 
 (c) 3 (d) – 3 
17. If (a + b)/c = 6/5 and (b + c)/a = 9/2, then what 
is the value of (a + c)/b? 
 Ùeefo (a + b)/c = 6/5 Deewj (b + c)/a = 9/2 nw, lees (a + 
c)/b keâe ceeve keäÙee nw? 
 (a) 9/5 (b) 11/7 
 (c) 7/11 (d) 7/4 
18. If x
3
 + y
3
 + z
3
 = 3(1+xyz), P = y + z – x, Q = z + 
x –y and R = x + y – z, then what is the value of 
p
3
+Q
3
+R
3
–3PQR? 
 Ùeefo x
3
 + y
3
 + z
3
 = 3(1+xyz), P = y + z – x, Q = z 
+ x –y Deewj R = x + y – z, nw, lees p
3
+Q
3
+R
3
–3PQR 
keâe ceeve keäÙee nw? 
 (a) 9 (b) 8 
 (c) 12 (d) 6 
19. If x
1
x
2
x
3
 = 4(4+x
1
+x
2
+x
3
), then what is the value 
of [1/(2+x
1
)] + [1/(2+x
2
)] + [1/(2+x
3
)]? 
 Ùeefo x
1
x
2
x
3
 = 4(4+x
1
+x
2
+x
3
), nes, lees [1/(2+x
1
)] + 
[1/(2+x
2
)] + [1/(2+x
3
)] keâe ceeve keäÙee nw? 
 (a) 1 (b) 1/2 
 (c) 2 (d) 1/3 
20. If a and ß are the roots of equation x
2
–x+1= 0, 
then which equation will have roots a
3
 and ß
3
? 
 Ùeefo a leLee ß meceerkeâjCe x
2
–x+1=0 kesâ cetue nQ, lees 
efkeâme meceerkeâjCe kesâ cetue a
3
 leLee ß
3
 neWies? 
 (a) x
2 
+ 2x + 1 = 0 
 (b) x
2 
– 2x – 1 = 0 
 (c) x
2 
+ 3x – 1 = 0 
 (d) x
2 
– 3x + 1 = 0 
21. If 3x + 5y + 7z = 49 and 9x + 8y + 21z = 126, 
then what is the value of y? 
 Ùeefo 3x + 5y + 7z = 49 leLee 9x + 8y + 21z = 126, 
nw, lees y keâe ceeve keäÙee nw? 
 (a) 4 (b) 2 
 (c) 3 (d) 5 
22. Cost of 4 pens, 6 note books and 9 files is Rs. 
305. Cost of 3 pens, 4 notebooks and 2 files is 
Rs. 145. What is the cost (in Rs) of 5 pens, 8 
notebooks and 16 files? 
 4 keâuece, 6 veesšyegkeâ leLee 9 HeâeFue keâe cetuÙe 305 ®0 
nw~ 3 keâuece, 4 veesšyegkeâ leLee 2 HeâeFue keâe cetuÙe 145 
®0 nw~ 5 keâuece, 8 veesšyegkeâ leLee 16 HeâeFue keâe cetuÙe 
(®0 ceW) keäÙee nw? 
 (a) 415 
 (b) 465 
 (c) 440 
 (d) Cannot be determined / %eele veneR efkeâÙee pee mekeâlee 
 
   
23. ABC is a right angled triangle. ?BAC = 90
0
 
and ?ACB = 60
0
. What is the ratio of the 
circum radius of the triangle to the side AB? 
 ABC Skeâ mecekeâesCe ef$eYegpe nw~ ?BAC = 90
0
 leLee 
?ACB = 60
0
 nw~ ef$eYegpe keâer heefjef$epÙee keâe Yegpee AB 
mes keäÙee Devegheele nw? 
 (a) 1 : 2 (b) 1 : v3 
 (c) 2 : v3 (d) 2 : 3 
24. In the given figure, ABCD is a square whose 
side is 4 cm. P is a point on the side AD. What 
is the minimum value (in cm) of BP + CP? 
 oer ieF& Deeke=âefle ceW, ABCD Skeâ Jeie& nw efpemekeâer Yegpee 4 
mes.ceer. nw~ Yegpee AD hej P Skeâ efyevog nw~ BP + CP keâe 
vÙetvelece ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 4v5 (b) 4v4 
 (c) 6v3 (d) 4v6 
25. Triangle ABC is similar to triangle PQR and 
AB : PQ = 2 : 3. AD is the median to the side 
BC in triangle ABC and PS is the median to the 
side QR in triangle PQR. What is the value of 
(BD/QS)
2
? 
 ef$eYegpe ABC, ef$eYegpe PQR kesâ mece¤he nw leLee AB : 
PQ = 2 : 3 nw~ AD, ef$eYegpe ABC ceW Yegpee BC hej Skeâ 
ceeefOÙekeâe nw leLee PS, ef$eYegpe PQR ceW Yegpee QR hej 
Skeâ ceeefOÙekeâe nw~ (BD/QS)
2  
keâe ceeve keäÙee nw? 
 (a) 3/5 (b) 4/9 
 (c) 2/3 (d) 4/7 
26. In the given figure, B and C are the centres of 
the two circles. ADE is the common tangent to 
the two circles. If the ratio of the radius of both 
the circles is 3 : 5 and AC = 40, then what is the 
value of DE? 
 oer ieF& Deeke=âefle ceW, B leLee C oes Je=òeeW kesâ kesâvõ nQ~ 
ADE oesveeW Je=òeeW keâer Skeâ GYeÙeefve<" mheMe& jsKee nw~ Ùeefo 
oesveeW Je=òeeW keâer ef$epÙeeDeeW keâe Devegheele 3 : 5 nw leLee 
AC = 40 nw, lees DE keâe ceeve keäÙee nw? 
 
 (a) 3v15 (b) 5v15 
 (c) 6v15 (d) 4v15 
27. In the given figure, AB = 30 cm and CD = 24 
cm. What is the value (in cm) of MN? 
 oer ieF& Deeke=âefle ceW, AB = 30 mes.ceer. leLee CD = 24 
mes.ceer. nw~ MN keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 18 (b) 9 
 (c) 12 (d) 15 
28. AB and AC are the two tangents to a circle 
whose radius is 6 cm. If ?BAC = 60
0
, then what 
is the value (in cm) of v(AB
2
 + AC
2
)? 
 AB Deewj AC Skeâ Je=òe hej oes mheMe& jsKeeSB nQ efpemekeâer 
ef$epÙee 6 mes.ceer. nw~ Ùeefo ?BAC = 60
0 
nw, lees v(AB
2
 + 
AC
2
) keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 (a) 6v6 (b) 4v6 
 (c) 9v3 (d) 8v3 
29. In the given figure, ABC is a right angled 
triangle. ?ABC = 90
0 
and ?ACB = 60
0
. If the 
radius of the smaller circle is 2 cm, then what is 
the radius (in cm) of the larger circle? 
 oer ieF& Deeke=âefle ceW, ABC Skeâ mecekeâesCe ef$eYegpe nw~ 
?ABC = 90
0 
leLee ?ACB = 60
0
 nw~ Ùeefo Úesšs Je=òe 
keâer ef$epÙee 2 mes.ceer. nw, lees yeÌ[s Je=òe keâer ef$epÙee (mes.ceer. 
ceW) keäÙee nw? 
 
 (a) 4 (b) 6 
 (c) 4.5 (d) 7.5 
30. In the given figure, O is centre of the circle. 
Circle has 3 tangents. If ?QPR = 45
0
, then 
what is the value (in degrees) of ?QOR? 
 oer ieF& Deeke=âefle ceW, O Je=òe keâe kesâvõ nw~ Je=òe hej 3 mheMe& 
jsKeeSB nQ~ Ùeefo ?QPR = 45
0 
nw, lees ?QOR keâe ceeve 
(ef[«eer ceW) keäÙee nw? 
 
 (a) 67.5 (b) 72 
 (c) 78.5 (d) 65 
 
   
31. In the given figure, two identical circles of 
radius 4 cm touch each other. A and B are 
the centres of the two circles. If RQ is a 
tangent to the circle, then what is the length 
(in cm) of RQ? 
 oer ieF& Deeke=âefle ceW, oes meceeve Je=òe efpevekeâer ef$epÙee 4 
mesceer. nQ Skeâ otmejs keâes mheMe& keâj jns nQ~ oesveeW Je=òeeW kesâ 
kesâvõ A leLee B nQ~ Ùeefo RQ Je=òe hej Skeâ mheMe&jsKee nw, 
lees RQ keâer uecyeeF& (mesceer. ceW) keäÙee nw? 
 
 (a) 3v3 (b) 2v6 
 (c) 4v2 (d) 6v2 
32. The radius of two circles is 3 cm. The distance 
between the centres of the circles is 10 cm. 
What is the ratio of the length of direct 
common tangent to the length of the transverse 
common tangent? 
 oes Je=òeeW keâer ef$epÙeeSB 3 mesceer0 leLee 4 mesceer0 nQ~ oesveeW 
Je=òeeW kesâ kesâvõeW kesâ ceOÙe keâer otjer 10 mesceer0 nw~ GYeÙeefve… 
DevegmheMe& jsKee keâer uecyeeF& keâe DevegØemLe DevegmheMe& jsKee 
keâer uecyeeF& mes Devegheele keäÙee nw? 
 (a) v51 : v68 (b) v33 : v17 
 (c) v66 : v51 (d) v28 : v17 
33. ABC is a triangle, AB = 5 cm, AC = v41 cm and 
BC = 8 cm, AD is perpendicular to BC. What is 
the area (in cm
2
) of triangle ABD? 
 ABC Skeâ ef$eYegpe nw~ AB = 5 mesceer0, AC = v41 
mesceer0 leLee BC = 8 mesceer0 nw~ AD, BC hej Skeâ 
meceuecye nw~ ef$eYegpe ABD keâe #es$eheâue (mesceer0
2
 ceW) 
keäÙee nw? 
 (a) 12 (b) 6 
 (c) 10 (d) 20 
34. In the given figure, PQR is a triangle and 
quadrilateral ABCD is inscribed in it. QD = 2 
cm, QC = 5 cm, CR = 3 cm, BR = 4 cm, PB = 6 
cm, PA = 5 cm and AD = 3 cm. What is the 
area (in cm
2
) of the quadrilateral ABCD? 
 oer ieF& Deeke=âefle ceW, PQR Skeâ ef$eYegpe nw leLee ÛelegYeg&pe 
ABCD GmeceW Debefkeâle efkeâÙee ieÙee nw~ QD = 2 mesceer0, 
QC = 5 mesceer0, CR = 3 mesceer0, BR = 4 mesceer0, PB 
= 6 mesceer, PA = 5 mesceer0 leLee AD = 3 mesceer0 nQ~ 
ÛelegYeg&pe ABCD keâe #es$eheâue (mesceer.
2
 ceW) keäÙee nw? 
 
 (a) (23v21)/4 (b) (15v21)/4 
 (c) (17v21)/5 (d) (23v21)/5 
35. In the given figure, ABCD is a square of side 14 
cm. E and F are mid points of sides AB and DC 
respectively. EPF is a semicircle whose 
diameter is EF. LMNO is a square. What is the 
area (in cm
2
) of the shaded region? 
 oer ieF& Deeke=âefle ceW, ABCD 14 mesceer0 Yegpee Jeeuee Skeâ 
Jeie& nw~ E leLee F ›eâceMe: AB leLee DC Yegpee kesâ ceOÙe 
efyevog nQ~ EPF, Skeâ DeOe&Je=òe nw efpemekeâe JÙeeme EF nw~ 
LMNO Skeâ Jeie& nw~ ÚeÙeebefkeâle Yeeie keâe #es$eheâue 
(mesceer0
2
 ceW) keäÙee nw? 
 
 (a) 108.5 (b) 94.5 
 (c) 70 (d) 120 
36. In the given figure, ABCDEF is a regular 
hexagon whose side is 6 cm. APF, QAB, DCR 
and DES are equilateral triangles. What is the 
area (in cm
2
) of the shaded region? 
 oer ieF& Deeke=âefle ceW, ABCDEF Skeâ mece <ešdYegpe nw 
efpemekeâer Yegpee 6 mesceer0 nw~ APF, QAB, DCR leLee 
DES meceyeeng ef$eYegpe nQ~ DeeÛÚeefole Yeeie keâe #es$eheâue 
(mesceer0
2
 ceW) keäÙee nw? 
 
 (a) 24v3 (b) 18v3 
 (c) 72v3 (d) 36v3 
Page 5


 
  
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
 (Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 17-2-2018] [Time : 10 AM to 12 PM 
1. What is the unit digit of the sum of first 111 
whole numbers? 
 ØeLece 111 hetCe& mebKÙeeDeeW kesâ Ùeesie keâe FkeâeF& Debkeâ keäÙee 
nw? 
 (a) 4 (b) 6 
 (c) 5 (d) 0 
2. How many 100 digit positive number are 
there? 
 100 DebkeâeW keâer efkeâleveer Oeveelcekeâ mebKÙeeSB nQ? 
 (a) 9 × 10
99
 (b) 9 × 10
100 
 (c) 10100 (d) 11 × 10
98 
3. What is the value of 
5.6 0.36 0.42 3.2
?
0.8 2.1
× + ×
×
 
 
5.6 0.36 0.42 3.2
0.8 2.1
× + ×
×
 keâe ceeve keäÙee nw? 
 (a) 2 (b) 1 
 (c) 3 (d) 3/2 
4. What is the value of 
 
–
– – –
3 3 3
2 2 2
(1.2) (0.8) (0.7) 2.016
?
(1.35) (1.2) (0.8) (0.7) 0.96 0.84 0.56
+ +
? ? + +
? ?
 
 
–
– – –
3 3 3
2 2 2
(1.2) (0.8) (0.7) 2.016
?
(1.35) (1.2) (0.8) (0.7) 0.96 0.84 0.56
+ +
? ? + +
? ?
 
 keâe ceeve keäÙee nw? 
 (a) 1/4 (b) 1/2 
 (c) 1 (d) 2 
5. What is the unit digit of  
 (217)
413
×(819)
547
×(414)
624
×(342)
812
? 
 (217)
413
×(819)
547
×(414)
624
×(342)
812
 keâe FkeâeF& Debkeâ 
keäÙee nw? 
 (a) 2 (b) 4 
 (c) 6 (d) 8 
6. What is the value of 
1 1
S
1 3 5 1 4
= + +
× × ×
 
 
1 1 1 1
...
3 5 7 4 7 5 7 9 7 10
+ + + +
× × × × × ×
upto 20 
terms, then what is the value of S? 
 
1 1 1 1
S
1 3 5 1 4 3 5 7 4 7
= + + + +
× × × × × ×
 
 
1 1
...
5 7 9 7 10
+ +
× × ×
20 heoeW lekeâ nQ, lees S keâe ceeve 
keäÙee nw? 
 (a) 6179/15275 (b) 6070/14973 
 (c) 7191/15174 (d) 5183/16423 
7. Which of the following is TRUE? 
 efvecveefueefKele ceW mes keâewve-mee melÙe nw? 
 I. 
3 4
1 1 1
12 29 5
> > 
 II. 
3 4
1 1 1
29 12 5
> > 
 III. 
3 4
1 1 1
5 12 29
> > 
 IV. 
3 4
1 1 1
5 29 12
> > 
 (a) Only I / kesâJeue  I  
 (b) Only II / kesâJeue  II  
 (c) Only III / kesâJeue  III  
 (d) Only IV / kesâJeue  IV  
8. N is the largest two digit number, which when 
divided by 3, 4 and 6 leaves the remainder 1, 2 
and 4 respectively. What is the remainder 
when N is divided by 5? 
 oes DebkeâeW keâer Skeâ meyemes yeÌ[er mebKÙee N nw, efpemes peye 3, 
4 leLee 6 mes efJeYeeefpele efkeâÙee peelee nw lees Mes<eHeâue 
›eâceMe: 1, 2 leLee 4 Deelee nw~ N keâes 5 mes efJeYeeefpele 
keâjves hej Mes<eHeâue keäÙee nw? 
 (a) 4 (b) 2 
 (c) 0 (d) 1 
9. Which of the following is TRUE? 
 efvecveefueefKele ceW mes keâewve-mee melÙe nw? 
 I. 
3 4
11 7 45 > > 
 II. 
3 4
7 11 45 > > 
 III. 
3 4
7 45 11 > > 
 IV. 
3 4
45 7 11 > > 
 
   
 (a) Only I / kesâJeue I  
 (b) Only II / kesâJeue II  
 (c) Only III / kesâJeue III  
 (d) Only IV / kesâJeue IV  
10. A and B are positive integers. If A + B + AB = 
65, then what is the difference between A and B 
(A, B = 15)? 
 A leLee B Oeveelcekeâ hetCeeËkeâ nw~ Ùeefo A+B+AB = 65 nw, 
lees A leLee B kesâ ceOÙe Deblej keäÙee nw (A, B = 15)? 
 (a) 3 (b) 4 
 (c) 5 (d) 6 
11. What is the value of 14
3
 + 16
3
 + 18
3
 + .... + 30
3
? 
 14
3
 + 16
3
 + 18
3
 + ....... + 30
3
 keâe ceeve keäÙee nw? 
 (a) 134576 (b) 120212 
 (c) 115624 (d) 111672 
12. What is the value of 
 4600 540 1280 250 36 ? + + + + 
 4600 540 1280 250 36 ? + + + + keâe ceeve 
keäÙee nw? 
 (a) 69 (b) 68 
 (c) 70 (d) 72 
13. If x + y + z = 0, then what is the value of 
(3y
2
+x
2
+z
2
)/(2y
2
–xz)? 
 Ùeefo x + y + z = 0 nes, lees (3y
2
 + x
2
 + z
2
)/(2y
2
–xz) 
keâe ceeve keäÙee nw? 
 (a) 2 (b) 1 
 (c) 3/2 (d) 5/3 
14. If P = 7+4v3 and PQ = 1, then what is the value 
of 1/p
2
 + 1/Q
2
? 
 Ùeefo P = 7+4v3 leLee PQ = 1 nw, lees 1/p
2
 + 1/Q
2 
keâe 
ceeve keäÙee nw? 
 (a) 196 (b) 194 
 (c) 206 (d) 182 
15. If a
3
+3a
2
+9a = 1, then what is the value of a
3
 + 
(3/a)? 
 Ùeefo a
3
+3a
2
+9a = 1 nes, lees a
3
 + (3/a) keâe ceeve keäÙee 
nw? 
 (a) 31 (b) 26 
 (c) 28 (d) 24 
16. x, y and z are real numbers. If x
3
+y
3
+z
3
 = 13, x 
+ y + z = 1 and xyz = 1, then what is the value 
of xy + yz + zx? 
 x, y leLee z JeemleefJekeâ mebKÙeeSB nQ~ Ùeefo  x
3
+y
3
+z
3
 = 
13, x + y + z = 1 leLee xyz = 1 nw, lees xy + yz + zx 
keâe ceeve keäÙee nw? 
 (a) – 1 (b) 1 
 (c) 3 (d) – 3 
17. If (a + b)/c = 6/5 and (b + c)/a = 9/2, then what 
is the value of (a + c)/b? 
 Ùeefo (a + b)/c = 6/5 Deewj (b + c)/a = 9/2 nw, lees (a + 
c)/b keâe ceeve keäÙee nw? 
 (a) 9/5 (b) 11/7 
 (c) 7/11 (d) 7/4 
18. If x
3
 + y
3
 + z
3
 = 3(1+xyz), P = y + z – x, Q = z + 
x –y and R = x + y – z, then what is the value of 
p
3
+Q
3
+R
3
–3PQR? 
 Ùeefo x
3
 + y
3
 + z
3
 = 3(1+xyz), P = y + z – x, Q = z 
+ x –y Deewj R = x + y – z, nw, lees p
3
+Q
3
+R
3
–3PQR 
keâe ceeve keäÙee nw? 
 (a) 9 (b) 8 
 (c) 12 (d) 6 
19. If x
1
x
2
x
3
 = 4(4+x
1
+x
2
+x
3
), then what is the value 
of [1/(2+x
1
)] + [1/(2+x
2
)] + [1/(2+x
3
)]? 
 Ùeefo x
1
x
2
x
3
 = 4(4+x
1
+x
2
+x
3
), nes, lees [1/(2+x
1
)] + 
[1/(2+x
2
)] + [1/(2+x
3
)] keâe ceeve keäÙee nw? 
 (a) 1 (b) 1/2 
 (c) 2 (d) 1/3 
20. If a and ß are the roots of equation x
2
–x+1= 0, 
then which equation will have roots a
3
 and ß
3
? 
 Ùeefo a leLee ß meceerkeâjCe x
2
–x+1=0 kesâ cetue nQ, lees 
efkeâme meceerkeâjCe kesâ cetue a
3
 leLee ß
3
 neWies? 
 (a) x
2 
+ 2x + 1 = 0 
 (b) x
2 
– 2x – 1 = 0 
 (c) x
2 
+ 3x – 1 = 0 
 (d) x
2 
– 3x + 1 = 0 
21. If 3x + 5y + 7z = 49 and 9x + 8y + 21z = 126, 
then what is the value of y? 
 Ùeefo 3x + 5y + 7z = 49 leLee 9x + 8y + 21z = 126, 
nw, lees y keâe ceeve keäÙee nw? 
 (a) 4 (b) 2 
 (c) 3 (d) 5 
22. Cost of 4 pens, 6 note books and 9 files is Rs. 
305. Cost of 3 pens, 4 notebooks and 2 files is 
Rs. 145. What is the cost (in Rs) of 5 pens, 8 
notebooks and 16 files? 
 4 keâuece, 6 veesšyegkeâ leLee 9 HeâeFue keâe cetuÙe 305 ®0 
nw~ 3 keâuece, 4 veesšyegkeâ leLee 2 HeâeFue keâe cetuÙe 145 
®0 nw~ 5 keâuece, 8 veesšyegkeâ leLee 16 HeâeFue keâe cetuÙe 
(®0 ceW) keäÙee nw? 
 (a) 415 
 (b) 465 
 (c) 440 
 (d) Cannot be determined / %eele veneR efkeâÙee pee mekeâlee 
 
   
23. ABC is a right angled triangle. ?BAC = 90
0
 
and ?ACB = 60
0
. What is the ratio of the 
circum radius of the triangle to the side AB? 
 ABC Skeâ mecekeâesCe ef$eYegpe nw~ ?BAC = 90
0
 leLee 
?ACB = 60
0
 nw~ ef$eYegpe keâer heefjef$epÙee keâe Yegpee AB 
mes keäÙee Devegheele nw? 
 (a) 1 : 2 (b) 1 : v3 
 (c) 2 : v3 (d) 2 : 3 
24. In the given figure, ABCD is a square whose 
side is 4 cm. P is a point on the side AD. What 
is the minimum value (in cm) of BP + CP? 
 oer ieF& Deeke=âefle ceW, ABCD Skeâ Jeie& nw efpemekeâer Yegpee 4 
mes.ceer. nw~ Yegpee AD hej P Skeâ efyevog nw~ BP + CP keâe 
vÙetvelece ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 4v5 (b) 4v4 
 (c) 6v3 (d) 4v6 
25. Triangle ABC is similar to triangle PQR and 
AB : PQ = 2 : 3. AD is the median to the side 
BC in triangle ABC and PS is the median to the 
side QR in triangle PQR. What is the value of 
(BD/QS)
2
? 
 ef$eYegpe ABC, ef$eYegpe PQR kesâ mece¤he nw leLee AB : 
PQ = 2 : 3 nw~ AD, ef$eYegpe ABC ceW Yegpee BC hej Skeâ 
ceeefOÙekeâe nw leLee PS, ef$eYegpe PQR ceW Yegpee QR hej 
Skeâ ceeefOÙekeâe nw~ (BD/QS)
2  
keâe ceeve keäÙee nw? 
 (a) 3/5 (b) 4/9 
 (c) 2/3 (d) 4/7 
26. In the given figure, B and C are the centres of 
the two circles. ADE is the common tangent to 
the two circles. If the ratio of the radius of both 
the circles is 3 : 5 and AC = 40, then what is the 
value of DE? 
 oer ieF& Deeke=âefle ceW, B leLee C oes Je=òeeW kesâ kesâvõ nQ~ 
ADE oesveeW Je=òeeW keâer Skeâ GYeÙeefve<" mheMe& jsKee nw~ Ùeefo 
oesveeW Je=òeeW keâer ef$epÙeeDeeW keâe Devegheele 3 : 5 nw leLee 
AC = 40 nw, lees DE keâe ceeve keäÙee nw? 
 
 (a) 3v15 (b) 5v15 
 (c) 6v15 (d) 4v15 
27. In the given figure, AB = 30 cm and CD = 24 
cm. What is the value (in cm) of MN? 
 oer ieF& Deeke=âefle ceW, AB = 30 mes.ceer. leLee CD = 24 
mes.ceer. nw~ MN keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 18 (b) 9 
 (c) 12 (d) 15 
28. AB and AC are the two tangents to a circle 
whose radius is 6 cm. If ?BAC = 60
0
, then what 
is the value (in cm) of v(AB
2
 + AC
2
)? 
 AB Deewj AC Skeâ Je=òe hej oes mheMe& jsKeeSB nQ efpemekeâer 
ef$epÙee 6 mes.ceer. nw~ Ùeefo ?BAC = 60
0 
nw, lees v(AB
2
 + 
AC
2
) keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 (a) 6v6 (b) 4v6 
 (c) 9v3 (d) 8v3 
29. In the given figure, ABC is a right angled 
triangle. ?ABC = 90
0 
and ?ACB = 60
0
. If the 
radius of the smaller circle is 2 cm, then what is 
the radius (in cm) of the larger circle? 
 oer ieF& Deeke=âefle ceW, ABC Skeâ mecekeâesCe ef$eYegpe nw~ 
?ABC = 90
0 
leLee ?ACB = 60
0
 nw~ Ùeefo Úesšs Je=òe 
keâer ef$epÙee 2 mes.ceer. nw, lees yeÌ[s Je=òe keâer ef$epÙee (mes.ceer. 
ceW) keäÙee nw? 
 
 (a) 4 (b) 6 
 (c) 4.5 (d) 7.5 
30. In the given figure, O is centre of the circle. 
Circle has 3 tangents. If ?QPR = 45
0
, then 
what is the value (in degrees) of ?QOR? 
 oer ieF& Deeke=âefle ceW, O Je=òe keâe kesâvõ nw~ Je=òe hej 3 mheMe& 
jsKeeSB nQ~ Ùeefo ?QPR = 45
0 
nw, lees ?QOR keâe ceeve 
(ef[«eer ceW) keäÙee nw? 
 
 (a) 67.5 (b) 72 
 (c) 78.5 (d) 65 
 
   
31. In the given figure, two identical circles of 
radius 4 cm touch each other. A and B are 
the centres of the two circles. If RQ is a 
tangent to the circle, then what is the length 
(in cm) of RQ? 
 oer ieF& Deeke=âefle ceW, oes meceeve Je=òe efpevekeâer ef$epÙee 4 
mesceer. nQ Skeâ otmejs keâes mheMe& keâj jns nQ~ oesveeW Je=òeeW kesâ 
kesâvõ A leLee B nQ~ Ùeefo RQ Je=òe hej Skeâ mheMe&jsKee nw, 
lees RQ keâer uecyeeF& (mesceer. ceW) keäÙee nw? 
 
 (a) 3v3 (b) 2v6 
 (c) 4v2 (d) 6v2 
32. The radius of two circles is 3 cm. The distance 
between the centres of the circles is 10 cm. 
What is the ratio of the length of direct 
common tangent to the length of the transverse 
common tangent? 
 oes Je=òeeW keâer ef$epÙeeSB 3 mesceer0 leLee 4 mesceer0 nQ~ oesveeW 
Je=òeeW kesâ kesâvõeW kesâ ceOÙe keâer otjer 10 mesceer0 nw~ GYeÙeefve… 
DevegmheMe& jsKee keâer uecyeeF& keâe DevegØemLe DevegmheMe& jsKee 
keâer uecyeeF& mes Devegheele keäÙee nw? 
 (a) v51 : v68 (b) v33 : v17 
 (c) v66 : v51 (d) v28 : v17 
33. ABC is a triangle, AB = 5 cm, AC = v41 cm and 
BC = 8 cm, AD is perpendicular to BC. What is 
the area (in cm
2
) of triangle ABD? 
 ABC Skeâ ef$eYegpe nw~ AB = 5 mesceer0, AC = v41 
mesceer0 leLee BC = 8 mesceer0 nw~ AD, BC hej Skeâ 
meceuecye nw~ ef$eYegpe ABD keâe #es$eheâue (mesceer0
2
 ceW) 
keäÙee nw? 
 (a) 12 (b) 6 
 (c) 10 (d) 20 
34. In the given figure, PQR is a triangle and 
quadrilateral ABCD is inscribed in it. QD = 2 
cm, QC = 5 cm, CR = 3 cm, BR = 4 cm, PB = 6 
cm, PA = 5 cm and AD = 3 cm. What is the 
area (in cm
2
) of the quadrilateral ABCD? 
 oer ieF& Deeke=âefle ceW, PQR Skeâ ef$eYegpe nw leLee ÛelegYeg&pe 
ABCD GmeceW Debefkeâle efkeâÙee ieÙee nw~ QD = 2 mesceer0, 
QC = 5 mesceer0, CR = 3 mesceer0, BR = 4 mesceer0, PB 
= 6 mesceer, PA = 5 mesceer0 leLee AD = 3 mesceer0 nQ~ 
ÛelegYeg&pe ABCD keâe #es$eheâue (mesceer.
2
 ceW) keäÙee nw? 
 
 (a) (23v21)/4 (b) (15v21)/4 
 (c) (17v21)/5 (d) (23v21)/5 
35. In the given figure, ABCD is a square of side 14 
cm. E and F are mid points of sides AB and DC 
respectively. EPF is a semicircle whose 
diameter is EF. LMNO is a square. What is the 
area (in cm
2
) of the shaded region? 
 oer ieF& Deeke=âefle ceW, ABCD 14 mesceer0 Yegpee Jeeuee Skeâ 
Jeie& nw~ E leLee F ›eâceMe: AB leLee DC Yegpee kesâ ceOÙe 
efyevog nQ~ EPF, Skeâ DeOe&Je=òe nw efpemekeâe JÙeeme EF nw~ 
LMNO Skeâ Jeie& nw~ ÚeÙeebefkeâle Yeeie keâe #es$eheâue 
(mesceer0
2
 ceW) keäÙee nw? 
 
 (a) 108.5 (b) 94.5 
 (c) 70 (d) 120 
36. In the given figure, ABCDEF is a regular 
hexagon whose side is 6 cm. APF, QAB, DCR 
and DES are equilateral triangles. What is the 
area (in cm
2
) of the shaded region? 
 oer ieF& Deeke=âefle ceW, ABCDEF Skeâ mece <ešdYegpe nw 
efpemekeâer Yegpee 6 mesceer0 nw~ APF, QAB, DCR leLee 
DES meceyeeng ef$eYegpe nQ~ DeeÛÚeefole Yeeie keâe #es$eheâue 
(mesceer0
2
 ceW) keäÙee nw? 
 
 (a) 24v3 (b) 18v3 
 (c) 72v3 (d) 36v3 
 
   
37. Length and breadth of a rectangle are 8 cm 
and 6 cm respectively. The rectangle is cut on 
its four vertices such that the resulting figure is 
a regular octagon. What is the side (in cm) of 
the octagon? 
 Skeâ DeeÙele keâer uecyeeF& leLee ÛeewÌ[eF& ›eâceMe: 8 mesceer0 
leLee 6 mesceer0 nQ~ DeeÙele keâes Gmekesâ Ûeej Meer<eeX hej Fme 
Øekeâej keâeše peelee nw efkeâ efceueves Jeeueer Deeke=âefle Skeâ mece 
De„Yegpe nw~ De„Yegpe keâer Yegpee (mesceer0 ceW) keäÙee nw? 
 (a) 3(v11) – 7 
 (b) 5(v13) – 8 
 (c) 4(v3) – 11 
 (d) 6(v11) – 9 
38. In the given figure, radius of a circle is 14 2 
cm. PQRS is a square. EFGH, ABCD, WXYZ 
and LMNO are four identical squares. What is 
the total area (in cm
2
) of all the small squares? 
 oer ieF& Deeke=âefle ceW, Skeâ Je=òe keâer ef$epÙee 14 2 mesceer0 
nw~ PQRS Skeâ Jeie& nw~ EFGH, ABCD, WXYZ 
leLee LMNO Ûeej meceeve Jeie& nQ~ meYeer Úesšs JeieeX keâe 
kegâue #es$eheâue (mesceer0
2
 ceW) keäÙee nw? 
 
 (a) 31.36 (b) 125.44 
 (c) 62.72 (d) 156.8 
39. In the given figure, AB, AE, EF, FG and GB 
are semicircles. AB = 56 cm and AE = EF = FG 
= GB. What is the area (in cm
2
) of the shaded 
region? 
 oer ieF& Deeke=âefle ceW, AB, AE, EF, FG leLee GB 
DeOe&Je=òe nQ~ AB = 56 mesceer0 leLee AE = EF = FG 
= GB nQ~ ÚeÙeebefkeâle Yeeie keâe #es$eheâue (mesceer0
2
 ceW) 
keäÙee nw? 
 
 (a) 414.46 (b) 382.82 
 (c) 406.48 (d) 394.24 
40. A right prism has a square base with side of 
base 4 cm and the height of prism is 9 cm. The 
prism is cut in three parts of equal heights by 
two planes parallel to its base. What is the ratio 
of the volume of the top, middle and the bottom 
part respectively? 
 Skeâ mece efØepce keâe DeeOeej 4 mesceer0 Yegpee Jeeuee Skeâ 
Jeie& nw leLee efØepce keâer TBÛeeF& 9 mesceer0 nw~ efØepce keâes 
Gmekesâ DeeOeej kesâ meceeblej oes leueeW Éeje meceeve TBÛeeF& kesâ 
leerve YeeieeW ceW keâeše ieÙee nw~ ›eâceMe: Thejer ceOÙe leLee 
efveÛeues YeeieeW kesâ DeeÙeleve keâe Devegheele keäÙee nw? 
 (a) 1 : 8 : 27 (b) 1 : 7 : 19 
 (c) 1 : 8 : 20 (d) 1 : 7 : 20 
41. Radius of base of a hollow cone is 8 cm and its 
height is 15 cm. A sphere of largest radius is 
put inside the cone. What is the ratio of radius 
of base of cone to the radius of sphere? 
 Skeâ KeesKeues Mebkegâ kesâ DeeOeej ef$epÙee 8 mesceer0 leLee 
Gmekeâer TBÛeeF& 15 mesceer0 nQ~ meyemes yeÌ[er ef$epÙee Jeeuee 
Skeâ ieesuee Gme Mebkegâ ceW [euee peelee nw~ Mebkegâ kesâ DeeOeej 
keâer ef$epÙee keâe ieesues keâer ef$epÙee mes keäÙee Devegheele nw? 
 (a) 5 : 3 (b) 4 : 1 
 (c) 2 : 1 (d) 7 : 3 
42. The ratio of curved surface area of a right 
circular cylinder to the total area of its two 
bases is 2 : 1. If the total surface area of 
cylinder is 23100 cm
2
, then what is the volume 
(in cm
3
) of cylinder? 
 mece Je=òeekeâj yesueve kesâ Je›eâ he=…erÙe #es$eheâue keâe Devegheele 
Gmekesâ oesveeW DeeOeejeW kesâ kegâue #es$eheâue mes 2 : 1 nw~ Ùeefo 
yesueve keâe kegâue he=…erÙe #es$eheâue 23100 mesceer0
2
 nw, lees 
yesueve keâe DeeÙeleve (mesceer0
3
 ceW) keäÙee nw? 
 (a) 247200 (b) 269500 
 (c) 312500 (d) 341800 
43. A solid cylinder has radius of base 14 cm and 
height 15 cm. 4 identical cylinders are cut from 
each base as shown in the given figure. Height 
of small cylinder is 5 cm. What is the total 
surface area (in cm
2
) of the remaining part? 
 Skeâ "esme yesueve kesâ DeeOeej keâer ef$epÙee 14 mesceer0 leLee 
TBÛeeF& 15 mesceer0 nw~ pewmee efkeâ Deeke=âefle ceW oMee&Ùee ieÙee 
nw efkeâ Fmekesâ ØelÙeskeâ DeeOeej mes 4 meceeve yesueve keâešs nQ~ 
Úesšs yesueve keâer TBÛeeF& 5 mesceer. nw~ Mes<e Yeeie keâe kegâue 
he=…erÙe #es$eheâue (mesceer0
2
 ceW) keäÙee nw? 
 
 (a) 3740 (b) 3432 
 (c) 3124 (d) 2816